I think he calls every single time. It's possible he has AK and may fold, but other hands would he call the 3-bet and pot size flop bet with?

It seems like he made his decision on the flop to call you down regardless. Bear in mind that if he thinks you are a loose player that he's just willing to look you up with 20% of his stack.

If you put him AA/KK/QQ he's not folding AA/KK. Could he fold QQ with no overs 4-handed to you? That's the question.